In the first and third of his Munich Lectures in Economics, Kenneth Rogoff argued in favour of phasing out cash, at least high denominations and in some developed economies. (His second lecture covered financial crises, see my post.)
Rogoff is well aware that cash preserves privacy and he acknowledges that one should have very good reasons to advocate phasing it out. He believes that there are two: Tax evasion and the black economy on the one hand, and the zero lower bound on nominal interest rates on the other.
Based on earlier research (Rogoff 1998) he argues that withdrawing bank notes with high denominations (e.g., USD 100 bills, EUR 500 bills etc.) would increase the cost of evading taxes or engaging in the black economy sufficiently strongly as to raise tax revenues, and that increased tax revenues would more than compensate for any loss of seignorage.
The (close to) zero lower bound on nominal interest rates and the resulting constraints for monetary policy derive from the fact that cash pays a zero nominal interest rate. Rogoff emphasised the seminal contribution of Lebow (1993 Fed working paper) in identifying the problems connected with the zero lower bound as well as possible ways to address them. Rogoff added that earlier writers (e.g., Gesell, Goodfriend, Mankiw or Buiter) who suggested to relax the constraint by subjecting cash to depreciation missed the point. Rather than forcing a negative nominal interest rate upon cash one should eliminate it altogether. He also dismissed shifting to a higher inflation target to avoid the zero lower bound problem, pointing to the huge loss of credibility that central banks would suffer as a consequence. Among factors for the trend towards lower real interest rates, Rogoff emphasised demographics and the asset pricing consequences of rare disasters; he dismissed secular stagnation. He also discussed forward guidance in the form of price level targeting.
Rogoff suggests to replace cash by universal debit cards. He does not expect significant technical difficulties in the process and proposes to subsidise debit cards for low income households.